Evaluate −2² ÷ (−3/4)² ÷ 2³.

Step-by-step solution

1. 1

   Read the two powers carefully — the brackets decide the signs. In $-2^{2}$ there are no brackets around the $-2$, so the exponent applies only to the $2$:

   $-2^{2}=-(2^{2})=-4$

   But $\left(-\tfrac34\right)^{2}$ does have brackets, so the whole negative fraction is squared and the result is positive:

   $\left(-\frac34\right)^{2}=\frac{9}{16}$

2. 2

   Evaluate the last power.

   $2^{3}=8$

   so the expression is now $-4\div\tfrac{9}{16}\div 8$.

3. 3

   Do the divisions strictly left to right. Division by a fraction is multiplication by its reciprocal:

   $-4\div\frac{9}{16}=-4\times\frac{16}{9}=-\frac{64}{9}$

4. 4

   Divide by 8.

   $-\frac{64}{9}\div 8=-\frac{64}{72}=-\frac{8}{9}$

   $\boxed{-\dfrac89}$

5. 5

   Check the sign and the size. Exactly one factor is negative (the $-4$), so the answer must be negative ✓. In decimals, $-4\div 0.5625=-7.111$, and $-7.111\div 8=-0.889=-\tfrac89$ ✓. Had the first term been $(-2)^{2}=+4$, the answer would have been $+\tfrac89$ — which is why the bracket convention matters so much here.